A rolling bearing of the type with which the invention is concerned, as disclosed in DE-GM No. 7 434 724, has threaded holes in the flange of its outer ring which extend parallel to the bearing axis. A disadvantage of this rolling bearing is the fact that the threaded holes are located relatively close to the outer race or races of the outer ring so that they may weaken the outer ring considerably when the pitch diameter is greatly reduced in order to provide a compact rolling bearing, for example, for automobile wheels. During the operation of the rolling pulsating contact stress due to rolling is propagated from the rolling elements to the raceway of the outer ring and to the threads of the holes, often causing the threads to tear due to fatigue.